Wright earned first-team high school All-America honors from USA Today as a senior. He was also a Parade magazine All-American and was rated among the nation's top 10 defensive line prospects by Student Sports. He was a first-team Class 5A all-state, All-Greater Houston and all-district selection as a senior. He was a finalist for the Greater Houston Touchdown Club Player of the Year award that season during which he posted 104 tackles, six sacks, three fumble recoveries and two blocked point-after attempts in 2001. Wright played in the 2002 U.S. Army All-American Bowl alongside fellow Texas Longhorns Kasey Studdard and Justin Blalock.

Considered a five-star recruit by Rivals.com, Wright was ranked second among defensive tackle prospects in the nation (behind Haloti Ngata).[1]

Wright attended the University of Texas, where he played for coach Mack Brown's Texas Longhorns football team from 2002 to 2005. As a true freshman in 2002, he saw action in all 13 games and started nine. He was a first-team Freshman All-America selection by the Football Writers Association of America and The Sporting News. He earned Big 12 Defensive Freshman of the Year honors from the league's coaches, Fort Worth Star-Telegram, Houston Chronicle and The Sporting News. He shared the Longhorns' Outstanding Defensive Newcomer Award and ranked seventh on the team (first among true freshmen) in tackles (65), second in tackles for loss (13) and third in sacks (4.5) and quarterback pressures (15). He ranked in a third-place tie in tackles for loss and tied for fourth in sacks on Texas' freshman lists. Wright was a key member of a Longhorns defense that led the Big 12 and ranked eighth in the NCAA in pass defense (165.2 ypg), second in the conference and seventh in the nation in pass efficiency defense (96.1 rtg), eighth in the country in scoring defense (16.3 ppg) and 16th nationally in total defense (307.7 ypg). He performed particularly well in Big 12 action, posting 52 tackles (22 solo), 13 tackles for loss, 4.5 sacks, 10 pressures, one forced fumble and a blocked kick in eight league contests.

Wright started all 13 games at defensive tackle in 2003, earning consensus second-team All-Big 12 honors and sharing the Longhorns' Outstanding Defensive Lineman award. He recorded 80 tackles, a team-leading 7.5 sacks, 12 tackles for loss (tied for second on the team), a team-leading 30 pressures, three passes batted down and three forced fumbles. In four games against Top 25 teams, he registered a total of 31 tackles, three sacks, four tackles for loss and eight pressures. While only a sophomore, Wright was a key member of a defense which ranked ninth in the NCAA in pass defense (177.3 ypg), 25th in total defense (329.8 ypg) and 32nd in scoring defense (21.5 ppg).

Wright played in 11 games, making 10 starts, at defensive tackle as a junior in 2004. Despite battling an ankle injury for much of the season, he posted 36 tackles, a sack, three tackles for loss and seven quarterback pressures. He recorded 16 tackles, one tackle for loss and two pressures in five games versus Top 25 foes.

For his performance during the year, Wright was tabbed second-team All-American by The Sporting News and honorable mention All-American by Pro Football Weekly. He was also named first-team All-Big 12 by The Dallas Morning News and Fort Worth Star-Telegram. He earned second-team All-Big 12 honors from the Associated Press, the conference coaches, The Austin American-Statesman and the San Antonio Express-News. For the second straight year, he shared the team's Outstanding Defensive Lineman Award.

In 2005, Wright started all 13 games and posted 46 tackles, 14 tackles for loss, 4.5 sacks, 15 pressures, three passes defensed, one forced fumble and one fumble recovery. He was a finalist for the Lombardi Award and tabbed First-team All-America by the Walter Camp Football Foundation and the Associated Press. To end his career, he won the national championship in a Rose Bowl victory over Southern California.

Despite being widely regarded as a very good pro prospect and one of the best defensive tackles in the nation at Texas, Wright fell all the way to the seventh round and was selected by the Miami Dolphins with the 226th overall pick in the 2006 NFL Draft. It was later revealed that Wright had a torn rotator cuff, which he underwent surgery to repair in May 2006. In late July, Wright signed a four-year contract with the team.

Wright was not healthy enough to play during his rookie season. He spent all of 2006 on the non-football injury list.

Fully recovered from shoulder surgery, Wright practiced at defensive end as the backup to Vonnie Holliday during the team's April minicamps. Wright started his first game on October 7, 2007 against the Houston Texans. He played in 13 games with nine starts and registered 37 tackles, 1.5 sacks, a pass defensed and a fumble recovery.